Protein side-chain dynamics and residual conformational entropy.

1Department of Biochemistry and Molecular Biophysics, Columbia University, New York, New York 10032, USA.

Abstract

Changes in residual conformational entropy of proteins can be significant components of the thermodynamics of folding and binding. Nuclear magnetic resonance (NMR) spin relaxation is the only experimental technique capable of probing local protein entropy, by inference from local internal conformational dynamics. To assess the validity of this approach, the picosecond-to-nanosecond dynamics of the arginine side-chain N(epsilon)-H(epsilon) bond vectors of Escherichia coli ribonuclease H (RNase H) were determined by NMR spin relaxation and compared to the mechanistic detail provided by molecular dynamics (MD) simulations. The results indicate that arginine N(epsilon) spin relaxation primarily reflects persistence of guanidinium salt bridges and correlates well with simulated side-chain conformational entropy. In particular cases, the simulations show that the aliphatic part of the arginine side chain can retain substantial disorder while the guanidinium group maintains its salt bridges; thus, the N(epsilon)-H(epsilon) bond-vector orientation is conserved and side-chain flexibility is concealed from N(epsilon) spin relaxation. The MD simulations and an analysis of a rotamer library suggest that dynamic decoupling of the terminal moiety from the remainder of the side chain occurs for all five amino acids with more than two side-chain dihedral angles (R, K, E, Q, and M). Dynamic decoupling thus may represent a general biophysical strategy for minimizing the entropic penalties of folding and binding.

Structural determinants of Nε flexibility. (a) Relative side-chain solvent accessibility, calculated from the crystal structure of RNase H (PDB code 2RN2)39 using NACCESS,50 vs. experimental order parameters. (b) Average maximal fraction of time the Nε-Hε moiety (black) or the two Nη-Hη moieties (red) of an arginine participate in a salt bridge during a 20 ns trajectory. Standard errors of the mean of the salt-bridge fractions calculated over the eight 20 ns trajectories are shown. Dashed lines connect data points belonging to the same residue when needed for clarity.

Simulated (a) and experimental (b) arginine Nε order parameters vs. side-chain conformational entropy computed using a 20° integration mesh. Bootstrap standard errors of the entropies are shown. Error bars not shown are similar to or smaller than the plotted points.

Two-dimensional χ-angle plots for select arginine residues. For R27, R75 and R106, every 10th conformation from all eight 20 ns trajectories is shown; for R46 every 7th conformation from the extended 117 ns trajectory is shown. Conformations are color-coded with respect to the scalar product of the orientation of the Nε-Hε bond vector and its orientation in the first snapshot according to the color bar in the plot of R46. Representative structures of the respective arginine side chain and its interaction partner are shown, with salt bridges indicated by red dashed lines.

Two-dimensional χ-angle plot for R132. For clarity, every 10th conformation forming the salt bridge to E32 from all eight 20 ns trajectories is shown. Conformations are color-coded as in figure 5. In addition, the salt-bridge configuration of each conformation is indicated by the color of the corresponding rotamer label (red and blue). Representative structures are shown, with salt bridges indicated by red dashed lines.